12ed5
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Prime factorization
22 × 3
Step size
232.193¢
Octave
5\12ed5 (1160.96¢)
Twelfth
8\12ed5 (1857.54¢) (→2\3ed5)
Consistency limit
6
Distinct consistency limit
3
Special properties
| ← 11ed5 | 12ed5 | 13ed5 → |
Division of the 5th harmonic into 12 equal parts (12ed5) is related to the mothra temperament and the quadrawell temperament. The step size about 232.1928 cents, corresponding to 5.1681 edo. This tuning has a meantone fifth as the number of divisions of the 5th harmonic is multiple of 4.
Intervals
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | 0.0000 | exact 1/1 | |
| 1 | 232.1928 | 8/7 | |
| 2 | 464.3856 | 17/13 | |
| 3 | 696.5784 | meantone fifth (pseudo-3/2) | |
| 4 | 928.7712 | 65/38 | |
| 5 | 1160.9640 | 45/23 | |
| 6 | 1393.1569 | 38/17, 85/38 | meantone major second plus an octave |
| 7 | 1625.3497 | 23/9 | |
| 8 | 1857.5425 | 38/13 | |
| 9 | 2089.7353 | meantone major sixth plus an octave (pseudo-10/3) | |
| 10 | 2321.9281 | 65/17 | |
| 11 | 2554.1209 | 35/8 | |
| 12 | 2786.3137 | exact 5/1 | just major third plus two octaves |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -39 | -44 | -78 | +0 | -83 | +114 | +115 | -89 | -39 | +28 | +110 |
| Relative (%) | -16.8 | -19.1 | -33.6 | +0.0 | -35.9 | +49.1 | +49.6 | -38.3 | -16.8 | +12.1 | +47.2 | |
| Steps (reduced) |
5 (5) |
8 (8) |
10 (10) |
12 (0) |
13 (1) |
15 (3) |
16 (4) |
16 (4) |
17 (5) |
18 (6) |
19 (7) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -29 | +75 | -44 | +76 | -29 | +104 | +11 | -78 | +70 | -11 | -88 |
| Relative (%) | -12.4 | +32.3 | -19.1 | +32.8 | -12.4 | +44.9 | +4.6 | -33.6 | +30.0 | -4.7 | -37.8 | |
| Steps (reduced) |
19 (7) |
20 (8) |
20 (8) |
21 (9) |
21 (9) |
22 (10) |
22 (10) |
22 (10) |
23 (11) |
23 (11) |
23 (11) | |